Incorporating recycled aggregate concrete (RAC) into steel tubes provides a value-added and promising solution that can reduce environmental impact of waste concrete and meanwhile increase mechanical performances and durability of RAC material. Composite elastic modulus (CEM) is one of the most essential structural properties in the design and evaluation of recycled aggregate concrete-filled steel tubes (RACFST); however, it is found that available design provisions developed for conventional concrete members fail to predict the CEM of RACFST with good accuracy. This paper proposes a set of novel models to address this both research and engineering gap. A reliable experimental database is first established containing test results of circular RACFST beam and column specimens under axial and/or flexural loading. Based on this work, a mathematical approach, i.e., the grey correlation analysis, is used to evaluate the sensitivity influence of key parameters on the CEM of circular RACFST. It is demonstrated that the replacement ratio of recycled concrete aggregate (RCA) is less decisive on CEM than some other parameters such as the steel tube yield strength and the diameter-to-thickness ratio, but the RCA replacement ratio is still significant and should be considered for better representing the elastic stiffness of circular RACFST. Derivations based on elasticity theory are then presented to obtain an elastic stress-strain relationship and hence the expression of CEM of concentrically-loaded circular RACFST. A comparison between the theoretical results and the experimental ones is made to validate the proposed model. For easy use in routine design, two empirical models in compliance with design codes based on the superposition principle are also provided to estimate respectively the composite elastic compressive stiffness and flexural stiffness of circular RACFST. A good agreement between the predictions using the empirical models and the test data is exhibited.